What is the Greatest Common Factor of 74096 and 74114?

Greatest common factor (GCF) of 74096 and 74114 is 2.

GCF(74096,74114) = 2

We will now calculate the prime factors of 74096 and 74114, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74096 and 74114.

How to find the GCF of 74096 and 74114?

We will first find the prime factorization of 74096 and 74114. After we will calculate the factors of 74096 and 74114 and find the biggest common factor number .

Step-1: Prime Factorization of 74096

Prime factors of 74096 are 2, 11, 421. Prime factorization of 74096 in exponential form is:

74096 = 2⁴ × 11¹ × 421¹

Step-2: Prime Factorization of 74114

Prime factors of 74114 are 2, 37057. Prime factorization of 74114 in exponential form is:

74114 = 2¹ × 37057¹

Step-3: Factors of 74096

List of positive integer factors of 74096 that divides 74096 without a remainder.

1, 2, 4, 8, 11, 16, 22, 44, 88, 176, 421, 842, 1684, 3368, 4631, 6736, 9262, 18524, 37048

Step-4: Factors of 74114

List of positive integer factors of 74114 that divides 74096 without a remainder.

1, 2, 37057

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74096 and 74114. The biggest common factor number is the GCF number.
So the greatest common factor 74096 and 74114 is 2.

Also check out the Least Common Multiple of 74096 and 74114